{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length in cm</th>\n",
       "      <th>sepal width in cm</th>\n",
       "      <th>petal length in cm</th>\n",
       "      <th>petal width in cm</th>\n",
       "      <th>class label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length in cm  sepal width in cm  petal length in cm  \\\n",
       "145                 6.7                3.0                 5.2   \n",
       "146                 6.3                2.5                 5.0   \n",
       "147                 6.5                3.0                 5.2   \n",
       "148                 6.2                3.4                 5.4   \n",
       "149                 5.9                3.0                 5.1   \n",
       "\n",
       "     petal width in cm     class label  \n",
       "145                2.3  Iris-virginica  \n",
       "146                1.9  Iris-virginica  \n",
       "147                2.0  Iris-virginica  \n",
       "148                2.3  Iris-virginica  \n",
       "149                1.8  Iris-virginica  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_dict = {i:label for i,label in zip(\n",
    "                range(4),\n",
    "                  ('sepal length in cm',\n",
    "                  'sepal width in cm',\n",
    "                  'petal length in cm',\n",
    "                  'petal width in cm', ))}\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "df = pd.io.parsers.read_csv(\n",
    "    filepath_or_buffer='https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data',\n",
    "    header=None,\n",
    "    sep=',',\n",
    "    )\n",
    "df.columns = [l for i,l in sorted(feature_dict.items())] + ['class label']\n",
    "df.dropna(how=\"all\", inplace=True) # to drop the empty line at file-end\n",
    "\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"1.png\" alt=\"FAO\" width=\"690\" align=\"left\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import LabelEncoder\n",
    "\n",
    "X = df[['sepal length in cm','sepal width in cm','petal length in cm','petal width in cm']].values\n",
    "y = df['class label'].values\n",
    "\n",
    "enc = LabelEncoder()\n",
    "label_encoder = enc.fit(y)\n",
    "y = label_encoder.transform(y) + 1\n",
    "\n",
    "#label_dict = {1: 'Setosa', 2: 'Versicolor', 3:'Virginica'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"2.png\" alt=\"FAO\" width=\"290\" align=\"left\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分别求三种鸢尾花数据在不同特征维度上的均值向量 mi\n",
    "<img src=\"3.png\" alt=\"FAO\" width=\"390\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Vector class 1: [ 5.006  3.418  1.464  0.244]\n",
      "\n",
      "Mean Vector class 2: [ 5.936  2.77   4.26   1.326]\n",
      "\n",
      "Mean Vector class 3: [ 6.588  2.974  5.552  2.026]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.set_printoptions(precision=4)\n",
    "\n",
    "mean_vectors = []\n",
    "for cl in range(1,4):\n",
    "    mean_vectors.append(np.mean(X[y==cl], axis=0))\n",
    "    print('Mean Vector class %s: %s\\n' %(cl, mean_vectors[cl-1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 计算两个 4×4 维矩阵：类内散布矩阵和类间散布矩阵\n",
    "-  <img src=\"5.png\" alt=\"FAO\" width=\"330\" >\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "within-class Scatter Matrix:\n",
      " [[ 38.9562  13.683   24.614    5.6556]\n",
      " [ 13.683   17.035    8.12     4.9132]\n",
      " [ 24.614    8.12    27.22     6.2536]\n",
      " [  5.6556   4.9132   6.2536   6.1756]]\n"
     ]
    }
   ],
   "source": [
    "S_W = np.zeros((4,4))\n",
    "for cl,mv in zip(range(1,4), mean_vectors):\n",
    "    class_sc_mat = np.zeros((4,4))                  # scatter matrix for every class\n",
    "    for row in X[y == cl]:\n",
    "        row, mv = row.reshape(4,1), mv.reshape(4,1) # make column vectors\n",
    "        class_sc_mat += (row-mv).dot((row-mv).T)\n",
    "    S_W += class_sc_mat                             # sum class scatter matrices\n",
    "print('within-class Scatter Matrix:\\n', S_W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-  <img src=\"6.png\" alt=\"FAO\" width=\"430\" >"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "between-class Scatter Matrix:\n",
      " [[  63.2121  -19.534   165.1647   71.3631]\n",
      " [ -19.534    10.9776  -56.0552  -22.4924]\n",
      " [ 165.1647  -56.0552  436.6437  186.9081]\n",
      " [  71.3631  -22.4924  186.9081   80.6041]]\n"
     ]
    }
   ],
   "source": [
    "overall_mean = np.mean(X, axis=0)\n",
    "\n",
    "S_B = np.zeros((4,4))\n",
    "for i,mean_vec in enumerate(mean_vectors):  \n",
    "    n = X[y==i+1,:].shape[0]\n",
    "    mean_vec = mean_vec.reshape(4,1) # make column vector\n",
    "    overall_mean = overall_mean.reshape(4,1) # make column vector\n",
    "    S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)\n",
    "\n",
    "print('between-class Scatter Matrix:\\n', S_B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-  <img src=\"7.png\" alt=\"FAO\" width=\"230\" >"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Eigenvector 1: \n",
      "[[ 0.2049]\n",
      " [ 0.3871]\n",
      " [-0.5465]\n",
      " [-0.7138]]\n",
      "Eigenvalue 1: 3.23e+01\n",
      "\n",
      "Eigenvector 2: \n",
      "[[-0.009 ]\n",
      " [-0.589 ]\n",
      " [ 0.2543]\n",
      " [-0.767 ]]\n",
      "Eigenvalue 2: 2.78e-01\n",
      "\n",
      "Eigenvector 3: \n",
      "[[-0.7113]\n",
      " [ 0.0353]\n",
      " [-0.0267]\n",
      " [ 0.7015]]\n",
      "Eigenvalue 3: -5.76e-15\n",
      "\n",
      "Eigenvector 4: \n",
      "[[ 0.422 ]\n",
      " [-0.4364]\n",
      " [-0.4851]\n",
      " [ 0.6294]]\n",
      "Eigenvalue 4: 7.80e-15\n"
     ]
    }
   ],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))\n",
    "\n",
    "for i in range(len(eig_vals)):\n",
    "    eigvec_sc = eig_vecs[:,i].reshape(4,1)   \n",
    "    print('\\nEigenvector {}: \\n{}'.format(i+1, eigvec_sc.real))\n",
    "    print('Eigenvalue {:}: {:.2e}'.format(i+1, eig_vals[i].real))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 特征值与特征向量：\n",
    "- 特征向量：表示映射方向\n",
    "- 特征值：特征向量的重要程度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvalues in decreasing order:\n",
      "\n",
      "32.2719577997\n",
      "0.27756686384\n",
      "7.7995841654e-15\n",
      "5.76433252705e-15\n"
     ]
    }
   ],
   "source": [
    "#Make a list of (eigenvalue, eigenvector) tuples\n",
    "eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]\n",
    "\n",
    "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
    "eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)\n",
    "\n",
    "# Visually confirm that the list is correctly sorted by decreasing eigenvalues\n",
    "\n",
    "print('Eigenvalues in decreasing order:\\n')\n",
    "for i in eig_pairs:\n",
    "    print(i[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance explained:\n",
      "\n",
      "eigenvalue 1: 99.15%\n",
      "eigenvalue 2: 0.85%\n",
      "eigenvalue 3: 0.00%\n",
      "eigenvalue 4: 0.00%\n"
     ]
    }
   ],
   "source": [
    "print('Variance explained:\\n')\n",
    "eigv_sum = sum(eig_vals)\n",
    "for i,j in enumerate(eig_pairs):\n",
    "    print('eigenvalue {0:}: {1:.2%}'.format(i+1, (j[0]/eigv_sum).real))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "选择前两维特征"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix W:\n",
      " [[ 0.2049 -0.009 ]\n",
      " [ 0.3871 -0.589 ]\n",
      " [-0.5465  0.2543]\n",
      " [-0.7138 -0.767 ]]\n"
     ]
    }
   ],
   "source": [
    "W = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1)))\n",
    "print('Matrix W:\\n', W.real)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_lda = X.dot(W)\n",
    "assert X_lda.shape == (150,2), \"The matrix is not 150x2 dimensional.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EyMGDB8sffvhBDhs2TA4fPtxzoXgJF/tOtd69Qvoqs43/owWj0WgClrS0NBYv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\nInIEJiVERETkCExKiIiIyBH+PxU4etypL2pGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x206e6218908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "def plot_step_lda():\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X_lda[:,0].real[y == label],\n",
    "                y=X_lda[:,1].real[y == label],\n",
    "                marker=marker,\n",
    "                color=color,\n",
    "                alpha=0.5,\n",
    "                label=label_dict[label]\n",
    "                )\n",
    "\n",
    "    plt.xlabel('LD1')\n",
    "    plt.ylabel('LD2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title('LDA: Iris projection onto the first 2 linear discriminants')\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "            labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout\n",
    "    plt.show()\n",
    "\n",
    "plot_step_lda()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "# LDA\n",
    "sklearn_lda = LDA(n_components=2)\n",
    "X_lda_sklearn = sklearn_lda.fit_transform(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_scikit_lda(X, title):\n",
    "\n",
    "    ax = plt.subplot(111)\n",
    "    for label,marker,color in zip(\n",
    "        range(1,4),('^', 's', 'o'),('blue', 'red', 'green')):\n",
    "\n",
    "        plt.scatter(x=X[:,0][y == label],\n",
    "                    y=X[:,1][y == label] * -1, # flip the figure\n",
    "                    marker=marker,\n",
    "                    color=color,\n",
    "                    alpha=0.5,\n",
    "                    label=label_dict[label])\n",
    "\n",
    "    plt.xlabel('LD1')\n",
    "    plt.ylabel('LD2')\n",
    "\n",
    "    leg = plt.legend(loc='upper right', fancybox=True)\n",
    "    leg.get_frame().set_alpha(0.5)\n",
    "    plt.title(title)\n",
    "\n",
    "    # hide axis ticks\n",
    "    plt.tick_params(axis=\"both\", which=\"both\", bottom=\"off\", top=\"off\",  \n",
    "            labelbottom=\"on\", left=\"off\", right=\"off\", labelleft=\"on\")\n",
    "\n",
    "    # remove axis spines\n",
    "    ax.spines[\"top\"].set_visible(False)  \n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"bottom\"].set_visible(False)\n",
    "    ax.spines[\"left\"].set_visible(False)    \n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EyMGDB8sffvhBDhs2TA4fPtxzoXgJF/tOtd69Qvoqs43/owWj0WgClrS0NBYv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\nInIEJiVERETkCExKiIiIyBH+PxU4etypL2pGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x206e7bd6f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WrVtZv369VVtpaSkpKSlkZGRYtaelpdnIHWDZsmU28jlw4AApKSk2fYODgwkL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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x206e7bd6f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_step_lda()\n",
    "plot_scikit_lda(X_lda_sklearn, title='Default LDA via scikit-learn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
